Protein Engineering, Vol. 13, No. 9, 603-606,
September 2000
© 2000 Oxford University Press
Communication |
Prokink: a protocol for numerical evaluation of helix distortions by proline
1 Department of Physiology and Biophysics, Mount Sinai School of Medicine, One Gustave Levy Place, New York, NY 10029, USA
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Abstract |
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Proline residues are known to perturb the structure of helices by introducing a kink between the segments preceding and following the proline residue. The distortion of the helical structure results from the avoided steric clash between the ring of the proline at position (i) and the backbone carbonyl at position (i – 4), as well as the elimination of helix backbone H-bonds for the carbonyls at positions (i – 3) and (i – 4). Both the departure from the ideal helical pattern and the reduction in H-bond stabilization contribute to the observed flexibility of a proline-containing
-helix. The special local flexibility of the proline kink can confer an important role on the proline-containing helix in the conformational changes related to the function of the protein. As a useful tool in determining and evaluating the role of proline-induced flexibility and distortions in protein function, we present here a protocol to quantify the geometry of the distortion introduced in helices by prolines both as a time-averaged value and for individual `snapshots' along a molecular dynamics simulation.
Keywords: proline kink/transmembrane proteins
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Introduction |
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Proline residues are known to perturb the structure of helices by introducing a kink between the segment preceding and following the proline residue (Barlow and Thornton, 1988
; Ballesteros and Weinstein, 1992; Sankararamakrishnan and Vishweshwara, 1992). It is well known that the distortion of the helical structure produced by the proline results from the avoided steric clash between the ring and the backbone carbonyl at position (i – 4) [relative to the position (i) of the proline], as well as the elimination of helix backbone H-bonds for the carbonyls at positions (i – 3) and (i – 4) (Woolfson and Williams, 1990; Thornton et al., 1991; Sankararamakrishnan and Vishweshwara, 1992; Ballesteros and Weinstein, 1995). Both the departure from the helical pattern and the reduction in H-bond stabilization contribute to the observed flexibility of a proline-containing -helix. Thus, the geometry of the proline kink (PK) region in an -helix is characterized by backbone dihedral angles that deviate from -helical values (Barlow and Thornton, 1988). In solution, the backbone angles have been shown to vary (Pastore et al., 1989), in agreement with a calculated broad energy minimum related to the presence of the proline in the helix (Piela et al., 1987; Barlow and Thornton, 1988; Yun et al., 1991). This variability indicates that in the absence of specific interactions, a PK motif produces significant flexibility that enables a number of different conformations of the helix in that region (Pastore et al., 1989; Williams and Deber, 1991; Ballesteros and Weinstein, 1995).
The special local flexibility of the PK confers a dynamic behavior on the proline-containing helix that can be relevant in the conformational changes related to functional mechanisms of the protein. For example, the structural distortion of the -helix by a conserved proline has been shown to play a key role in the voltage-dependent gating mechanism of conexin32 (Ri et al., 1999). By mediating the propagation of conformational changes from one domain in the protein to another, the prolines can acquire a dynamic role in the interconversion of different protein states, as has been proposed in the activation mechanisms of G-protein coupled receptors (Luo et al., 1994; Ballesteros and Weinstein, 1995; Gether et al., 1997). Computational techniques attempting to simulate the dynamic behavior of proteins evaluate the conformational changes that can be related to such functional mechanisms of the proteins. An accurate quantification of the geometry of the distortion introduced in helices by prolines, recorded both on average and for individual `snapshots' along a molecular dynamics trajectory, can therefore provide a useful tool in determining and evaluating the role of proline-induced flexibility and distortions in protein function.
The PK has been defined previously in terms of a bend (Barlow and Thornton, 1988) and a twist (Ballesteros and Weinstein, 1992; Sankararamakrishnan and Vishweshwara, 1992). We describe here a practical geometric definition of helix distortions by the PK, and introduce an algorithm for numerical evaluation of the parameters describing the proline-kinked helix. This algorithm can be used to characterize the deviation from ideal helix geometry regardless of the reasons for the distortion.
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Methods |
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Definitions
The method quantifies three aspects of the helix's coordinates that are referenced to the proline-kinked helix itself, the bend angle, the wobble angle and the face shift, defined as shown in Figures 1 and 2. The definition of the PK involves two parts in the helix: from the N-terminus to the proline, the segment constitutes the `pre-proline' helix; the segment from the proline to the C-terminus is the `post-proline' helix.
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The bend angle (Figure 1C
) is the angle between the two parts when the helix is kinked along its axis. The wobble angle (Figure 1D) is the angle that defines the orientation of the post-proline helix in three-dimensional space, with respect to the pre-proline helix. The face shift (Figure 2) measures the distortion that causes a twisting of the helix `face' in such a way that amino acids that used to be on the same side (face) of the helix are shifted and are on different sides of the helix as a result of the bend. Note that the face shift is related to the bend and wobble angles, but it is nevertheless a useful descriptor because it makes reference to the internal rearrangement of the atoms involved directly in the distortion (i – 4 to i). The other two parameters, bend and wobble angle, describe directly the 3D orientation of the distortion. Taken together, the three descriptors provide a complete characterization of the PK in terms that can serve a functional context. The axis for the entire helix or its parts is defined and determined as in the CHARMM package (Brooks et al., 1983). Quantification
To quantify the change in the helix distortion parameters throughout the MD trajectory, the orientation must remain constant. This is accomplished by choosing common positions in the helices and placing them at similar positions in the coordinates systems by rotations and translations. As a starting point the proline -carbon is translated to the cartesian origin, as exemplified in Figure 1 for a transition between parts A and B. The unit vectors that define pre- and post-proline axes are defined at this origin. Rotations are performed so that the unit vector that defines the axis of the pre-proline helix is on the positive x-axis. (Figure 1B). For practical purposes each segment should be chosen to contain complete turns of helix, preferably a minimum of two turns (seven residues) in order to make the calculation reliable.
Wobble angle.
The calculation of the wobble angle requires a reorientation of the system that translates the center of the pre-proline helix to the positive x-axis (with y and z values equal to zero) and the proline -carbon to the positive y-axis (with x and z values equal to zero) (Figure 1C). With the pre-proline helix's axis on the x-axis and the pre-proline helix's center on the x-axis, a plane is defined that bisects this cylinder perpendicular to the x-axis. When this plane contains the point that defines the proline -carbon, it is the y,z-plane. The point where the y,z-plane bisects the axis of the pre-proline helix is the origin.
As shown in Figure 1D, the wobble angle is calculated as the angle between the projection of the vector that defines the axis of the post-proline helix on the y,z-plane, with the vector that connects the origin with the proline -carbon (this vector is in the y,z-plane). The measure ranges from –180 to 180°. The wobble angle is close to zero when the post-proline helix is bent so that its axis is moved towards the proline -carbon. It is close to –180 or 180° when the axis of the post-proline helix is moved away from the proline. The wobble angle is negative when the post-proline helix axis has a negative z value and it is positive for positive values of z (see Figure 1D).
Bend angle.
To calculate the bend angle, the coordinate system is rotated around the x-axis so that the axis of the post-proline helix is in the x,y-plane (Figure 1C). From this orientation, the angle between the axes of the two helices can be calculated. The bend angle ranges from 0 to 180°; the closer it is to 0°, the smaller is the bend in the helix.
Face shift.
To calculate the face shift, the pre-proline helix is left unaltered but the post-proline helix is rotated so that its axis is on the negative x-axis. For the purposes of this part of the analysis, the proline -carbon is included in the post-proline helix and undergoes this rotation. In this orientation, both portions of the helix, pre- and post-proline, have their axes on the x-axis.
The face shift is calculated as the angle illustrated in Figure 2: the angle is between the projection of the vector connecting the proline -carbon with the origin in the y,z-plane and the projection of the average of the vectors connecting the -carbons of the (i – 3) and (i – 4) amino acids with the origin in the y,z-plane (Figure 2). The values of the face shift range from –180 to 180°. Values closer to zero mean that the (i – 3) and (i – 4) amino acids are on either side of the proline -carbon. A negative face shift means that the helix is over-wound as a result of the proline kink, whereas positive values mean that the helix is under-wound (Figure 2).
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Results |
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Standards
To obtain a set of reference values for the helix parameters, we calculated the bend, wobble angle and face shift of an -helix (
= –65, 
= –40), a 3–10 helix ( = –60, = –30) and a 
-helix ( = –30, = –90).
When the algorithm is applied to two sequential fragments of a perfect -helix, the calculated bend angle is 1° and the face shift is 13° (Figure 3). When the helix is completely straight (the bend angle is 0°) the wobble angle cannot be calculated, since the post-proline helix axis does not have a projection in the y,z-plane. Even the smallest deviation from 0° allows a projection of the vector in the y,z-plane and yields a significant value for the wobble angle. Thus, wobble is a very sensitive measure of the position of the two axes, and becomes meaningful only when the bend angle is large enough. In practice, wobble angle values become meaningful for bend angles larger than 10°.
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The calculated face shift for the 3–10 helix is –26.4°, meaning that the helix is over-wound (Figure 3
), whereas the -helix yields a positive face shift value of 49.5°, indicating that it is under-wound (Figure 3). Illustrations
The algorithm was applied to several crystal structures obtained from the Brookhaven Protein Databank (PDB) (Berman et al., 2000) with resolution 
2 Å, containing apparently straight and bent helices. One example, the helix comprising residues 128–140 in myoglobin [accession code 1MBC (Kuriyan et al., 1986)], does not have a proline or other distortions of its helical character. The computed bend angle for this helix is 6° and the face shift 11.1°, both very close to the standard values calculated for an ideal -helix. Similarly, the helix containing residues 104–117 of subtilisin [1CSE (Bode et al., 1987)] has a bend angle of 6° and a face shift of 12.4°.
To evaluate the distortions induced by prolines we selected helices in cytrate syntase [2CTS (Remington et al., 1982)] and thermolysin [8TLN (Holland et al., 1992)]. Pro15 in 2CTS and Pro69 in 8TLN are in the middle of the -helices. The bend angle associated with Pro15 in 2CTS is 23.3°, the face shift is 38.6° (indicating that the helix is slightly underwound in the region of the proline kink) and the wobble angle is –131°. The Pro69-containing helix in 8TLN has a bend angle of 27.7°, a face shift of –4.1° and a wobble angle of –125.5°. The wobble angle determines the direction of the kink and indicates that, in this case, the presence of the proline is associated with an overwind of the helix.
As an example of the calculation along a molecular dynamics simulation (MD), we applied the algorithm to the characterization of the distortion induced by proline in transmembrane (TM) helix 6 of the 5HT2C receptor during 350 ps of the production run of an MD simulation (Figure 4).
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Algorithm
The algorithm presented here fully characterizes the three-dimensional geometry of the distortion introduced by proline in a helix, and is also able to characterize any deviation from ideality in helices of various types.
The program is written in FORTRAN 77. The input required to run the program is described below.
- Protein data file: this file contains the coordinates. The read format is I5, I5, A10, F10.5, F10.5, F10.5.
For an MD trajectory the structures are listed one after the other. The program uses a CRD format with the following characteristics:- The first line of the file is the first atom coordinates.
- The coordinates of the subsequent structures follow one another in the file without spaces, comments or any other separation between them.
- The first line of the file is the first atom coordinates.
- Center pre-proline helix file: the read format is 25X, F16.5, F16.5, F16.5. Each line of the input corresponds to the coordinates of the center of the pre-proline helix for each of the structures in the ensemble. The input file can be obtained directly from CHARMM with the following format (for five different structures of the molecule to be analyzed, e.g. from a trajectory):
- CENTER for helix 1 9.11963 12.16652 –11.05891
- CENTER for helix 1 9.13799 12.18377 –11.04533
- CENTER for helix 1 9.12429 12.19788 –11.05513
- CENTER for helix 1 9.09144 12.22649 –11.09036
- CENTER for helix 1 9.13554 12.16999 –11.08388
Note that `helix 1' is the arbitrary name that CHARMM uses to designate each helix under study.
- CENTER for helix 1 9.11963 12.16652 –11.05891
- Axes pre-proline helix file: the read format is 16X, F10.5, F10.5, F10.5. Each line corresponds to the unitary vector that defines the pre-proline helix axis for each structure in the ensemble (the example still contains five structures):
- HELIX AXIS: –0.058497 0.736802 0.628034
- HELIX AXIS: –0.058632 0.735659 0.628234
- HELIX AXIS: –0.055548 0.735889 0.628379
- HELIX AXIS: –0.056542 0.739882 0.622955
- HELIX AXIS: –0.057021 0.740794 0.622139
- HELIX AXIS: –0.058497 0.736802 0.628034
- Axes post-proline helix file: the read format is 16X, F10.5, F10.5, F10.5. This file has the same format as the `axes pre-proline helix' file (above).
- Atom number of the C- proline: entered interactively by the user.
- Atom number of the C- residue i – 4 from proline: entered interactively by the user.
- Atom number of the C- residue i – 3 from proline: entered interactively by the user.
- Total number of atoms in the protein: entered interactively by the user.
- Number of cycles in the study. This is the number of structures in a trajectory (e.g. from molecular dynamics). If there is only one structure this number will be equal to 1; in the example above, the number is 5. This data are also entered interactively by the user.
The documentation of the program, source code and executable are available on-line at http://transport.physbio.mssm.edu/prokink/.
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Notes |
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2 To whom correspondence should be addressed.E-mail: hweinstein{at}inka.mssm.edu
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Acknowledgments |
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We thank Dr Juan A.Ballesteros for suggesting this problem and for helpful discussions. This work was supported by NIH grants DA-12408, DA-12923 and DA-00060 (to H.W.). Benjamin B.Braunheim was supported by postdoctoral training grant T32 DA-07135. Computational support was provided by the Cornell Supercomputer Facility and the Advanced Scientific Computing Laboratory at the Frederick Cancer Research Facility of the National Cancer Institute.
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Received April 14, 2000; revised July 10, 2000; accepted July 10, 2000.
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